# Groups, Geometry, and Dynamics

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**Published online first: 2021-08-03**

**DOI: 10.4171/GGD/623**

Almost commuting matrices with respect to the rank metric

Gábor Elek^{[1]}and Łukasz Grabowski

^{[2]}(1) Lancaster University, UK

(2) Lancaster University, UK

We show that if $A_1,A_2,\ldots, A_n$ are square matrices, each of them is either unitary or self-adjoint, and they almost commute with respect to the rank metric, then one can find commuting matrices $B_1$, $B_2$, $\ldots$, $B_n$ that are close to the matrices $A_i$ in the rank metric.

*Keywords: *Rank metric, almost-commuting matrices, stability problems

Elek Gábor, Grabowski Łukasz: Almost commuting matrices with respect to the rank metric. *Groups Geom. Dyn.* Electronically published on August 3, 2021. doi: 10.4171/GGD/623 (to appear in print)